# Occupation Time of a Randomly Accelerated Particle on the Positive Half Axis: Results for the First Five Moments

@article{Burkhardt2017OccupationTO,
title={Occupation Time of a Randomly Accelerated Particle on the Positive Half Axis: Results for the First Five Moments},
author={Theodore W. Burkhardt},
journal={Journal of Statistical Physics},
year={2017},
volume={169},
pages={730-743}
}
• T. Burkhardt
• Published 4 August 2017
• Mathematics
• Journal of Statistical Physics
In the random acceleration process a point particle is accelerated by Gaussian white noise with zero mean. Although several fundamental statistical properties of the motion have been analyzed in detail, the statistics of occupation times is still not well understood. We consider the occupation or residence time $$T_+$$T+ on the positive x axis of a particle which is randomly accelerated on the unbounded x axis for a time t. The first two moments of $$T_+$$T+ were recently derived by Ouandji…
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## References

SHOWING 1-10 OF 34 REFERENCES

In the random acceleration process, a point particle is accelerated according to $\ddot{x}=\eta(t)$, where the right hand side represents Gaussian white noise with zero mean. We begin with the case
• Mathematics, Physics
• 2016
The random acceleration model is one of the simplest non-Markovian stochastic systems and has been widely studied in connection with applications in physics and mathematics. However, the occupation
• Mathematics
• 2001
We investigate the distribution of the time spent by a random walker to the right of a boundary moving with constant velocity v. For the continuous-time problem (Brownian motion), we provide a simple
Consider a randomly accelerated particle moving on the half-line x>0 with a boundary condition at x = 0 that respects the scale invariance of the equations of motion under x→λ3x, v→λv, t→λ2t. If the
• Mathematics
Physical review letters
• 1995
The aim in this Letter is to present the exact analytical solution to the mean exit time out of an interval for the displacement of an undamped free particle under the influence of a random acceleration.
We study the one-dimensional Burgers equation in the inviscid limit for Brownian initial velocity (i.e. the initial velocity is a two-sided Brownian motion that starts from the origin x=0). We obtain
• Mathematics
• 2010
We study the random acceleration model, which is perhaps one of the simplest, yet nontrivial, non-Markov stochastic processes, and is key to many applications. For this non-Markov process, we present
• Mathematics
• 1985
The authors obtain, for a Brownian particle in a uniform force field, the mean and asymptotic first-passage times as functions of the particle's initial position and velocity, with the recurrence
• Mathematics
• 2000
We consider a particle which is randomly accelerated by Gaussian white noise on the line 0<x<1, with absorbing boundaries at x = 0,1. Denoting the initial position and velocity of the particle by x0
• Mathematics
• 2013
In this review, we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such